Question

A rocket, initially at rest on the ground, accelerates straight
upward from rest with constant acceleration 44.1 m/s^2. The
acceleration period lasts for time 5.00 s until the fuel is
exhausted. After that, the rocket is in free fall.

Find the maximum height y_max reached by the rocket. Ignore air
resistance and assume a constant acceleration due to gravity equal
to 9.80 \rm{m/s^2} .